Non-equilibrium dynamics and chaos: from isolated to open quantum systems

Mondal, Debabrata (2026) Non-equilibrium dynamics and chaos: from isolated to open quantum systems. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Debabrata Mondal (18IP009)) 18IP009.pdf - Submitted Version Restricted to Repository staff only Download (6MB)

Abstract

Over recent decades, the non-equilibrium dynamics of both isolated and open quantum systems have attracted considerable attention, particularly the chaos, ergodicity and its deviation due to the quantum scarring phenomena. In the first part, we investigate an isolated system of two large spins described by the coupled top model to explore the connection between phase-space dynamics and local quantum ergodicity, including quantum scars. We also generalize this model to periodic driving and demonstrate the ergodicity and quantum scars of the 2-cycle. In rest of the thesis, we explore non-equilibrium and nonlinear dynamical phenomena in open quantum systems. Focusing on an atom-photon interacting system with two coupled cavities, we demonstrate the bistability of superradiant phases and onset of dissipative chaos. Moreover, in an array of coupled cavities, we study homogeneous phases and dissipative transition. Interestingly, we identify a chaotic regime, detected by the exponential growth of decorrelator, in which an ergodic steady state emerges, where collective quantities saturate while microscopic variables fluctuate strongly. We also demonstrate the existence of a chaotic steady state in the quantum domain using two coupled cavities. The chaotic mixing is revealed by rapid growth of the entropy and a fast decay of correlations. Remarkably, the steady state exhibits subsystem thermalization, and its statistical properties resemble those of random matrices. Chaos in the open anisotropic Dicke model is also identified, where spectral statistics fails to distinguish between regular and chaotic regimes. We characterize early-time transient chaos and fully-developed steady-state chaos, restoring quantum-classical correspondence, and show that spectral properties of Liouvillian may reflect early-time chaos. New results are important for the understanding of non-equilibrium dynamics and are accessible in ongoing experiments using ultracold atoms/cavity/circuit-QED setups, with relevance for quantum technologies and information processing.

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